Old English meltan "become liquid, consume by fire, burn up" (class III strong verb; past tense mealt, past participle molten), from Proto-Germanic *meltanan; fused with Old English gemæltan (Anglian), gemyltan (West Saxon) "make liquid," from Proto-Germanic *gamaltijan (source also of Old Norse melta "to digest"), both from PIE *meldh- (source also of Sanskrit mrduh "soft, mild," Greek meldein "to melt, make liquid," Latin mollis "soft, mild"), from root *mel- (1) "soft." Figurative use by c. 1200. Related: Melted; melting.
Of food, to melt in (one's) mouth is from 1690s. Melting pot is from 1540s; figurative use from 1855; popularized with reference to America by play "The Melting Pot" by Israel Zangwill (1908).